Chaos on the Billiard Table

Kapitel in diesem Buch

1. Frontmatter i
2. Contents vii
3. Introduction xi
4. A Dusty Discipline 1
5. How Puzzles Made Us Human 7
6. Let the Games Continue 14
7. Challenging Magic Squares for Magicians 26
8. Candy Crush’s Puzzling Mathematics 38
9. Chaos on the Billiard Table 47
10. Juggling with Numbers 63
11. The Quest for Randomness 69
12. Synthetic Biology, Real Mathematics 93
13. At the Far Ends of a New Universal Law 99
14. Twisted Math and Beautiful Geometry 107
15. Kenichi Miura’s Water Wheel, or The Dance of the Shapes of Constant Width 119
16. Dürer: Disguise, Distance, Disagreements, and Diagonals! 132
17. The Quaternion Group as a Symmetry Group 141
18. The Steiner- Lehmus Angle- Bisector Theorem 154
19. Key Ideas and Memorability in Proof 167
20. The Future of High School Mathematics 181
21. Demystifying the Math Myth: Analyzing the Contributing Factors for the Achievement Gap between Chinese and U.S. Students 187
22. The Pigeonhole Principle, Two Centuries before Dirichlet 201
23. A Prehistory of Nim 207
24. Gödel, Gentzen, Goodstein: The Magic Sound of a G- String 215
25. Global and Local 228
26. Mathematical Beauty, Understanding, and Discovery 241
27. A Guide for the Perplexed: What Mathematicians Need to Know to Understand Philosophers of Mathematics 265
28. Writing about Math for the Perplexed and the Traumatized 280
29. Is Big Data Enough? A Reflection on the Changing Role of Mathematics in Applications 293
30. The Statistical Crisis in Science 305
31. Statistics and the Ontario Lottery Retailer Scandal 319
32. Never Say Never 332
33. Contributors 337
34. Notable Writings 349
35. Acknowledgments 359
36. Credits 361